The given polynomial function is:
[tex]P(x)=a (x+b)^{2}(x-c) [/tex]
It is given that the P(x) has a zero at (-1,0) with multiplicity 2 and another zero at (4,0). So, b=1 and c=4 for the above equation. Substituting the values in equation of P(x), we get:
[tex]P(x)=a (x+1)^{2}(x-4)[/tex]
P(x) passes through the point (0,-12). Thus P(0) must be 12. Setting P(0) equal to 12, we get:
[tex]P(0)=a (0+1)^{2}(0-4) \\ \\
12=a(-4) \\ \\
a=-3 [/tex]
The polynomial thus becomes:
[tex]P(x)=-3 (x+1)^{2}(x-4)[/tex]
Therefore, leading coefficient, a , of the polynomial is -3. B option is the correct answer.
